OK, I poured some more of the drain cleaner last night. This morning I snaked again and a bit of gunk came out. I tried attaching some wire and backing out the snake. More gunk came out, but the wire twirled off the spiral cable wire. So I reattached some more wire and went back down with snake - a lot of gunk came out. I then flushed the pipe again with a sinkful of hot water and lots of Dawn, and that really did it. Lots of crud, and free flowing water!
I noticed in the gunk there were a number of greasy black flaps. My suspicion at this point is that the flaps were partially stuck to the walls of the pipe, but the unstuck sections blocked the smooth flow of water. The snake probably got through them OK, but once the snake was removed, the flaps and any other grease still there slowed the flow to a trickle.
Anyway, all is well, and I thank everyone for their suggestions.
Now, prevention. Besides limiting the grease, and using cold water when grease is flushed, are there any drain cleaners that are particularly effective in maintaining clean, less greasy pipes?
Thanks, Pete